Here are some basic reasons why not as i've tried things like this in another fps engine-
* you would need constant forward motion (and I don't mean constantly pressing the forward button.)if you stop you have a plane floating, may work with a helicopter...possibly.
* no climb and decend, you would have to hover at one height. Sure a jetpack can be scripted for this, but what about enemies.
*the mouse look would kill some effects of flying.moving forward and pointing strait down isnt very realistic.
There are some why nots. You would be better off looking for a flightsim engine.
hope that offerd some explaination.